Questions: Consider a charge in the presence of a magnetic field. When does it experience a force from that field? (A) Only if the charge is moving (B) Always (C) Only if the charge is not moving (D) Never

Solution Steps

The force experienced by a charge in a magnetic field is described by the Lorentz force law. According to this law, a charge \( q \) moving with velocity \( \mathbf{v} \) in a magnetic field \( \mathbf{B} \) experiences a force given by:

\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]

From the Lorentz force equation, it is clear that the force depends on the cross product of the velocity \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \). This implies that:

• If the charge is not moving (\( \mathbf{v} = 0 \)), the cross product is zero, and thus the force is zero.
• If the charge is moving (\( \mathbf{v} \neq 0 \)), the cross product is generally non-zero, and the charge experiences a force.

Given the conditions derived from the Lorentz force law:

• (A) Only if the charge is moving: This is correct because a stationary charge (\( \mathbf{v} = 0 \)) does not experience a force.
• (B) Always: This is incorrect because a stationary charge does not experience a force.
• (C) Only if the charge is not moving: This is incorrect because a stationary charge does not experience a force.
• (D) Never: This is incorrect because a moving charge does experience a force.

Final Answer